The Department of Education wants to fire two employees for covering up rumors – that later turned out unfounded – of a teacher having sex with students, officials said yesterday.

Ultimately, there was no proof that teacher Hillary Stringfellow had sex with two male students, 19 and 18, while she taught at Acorn HS for Social Justice in Brooklyn in 2005-06.

Stringfellow only had “inappropriate interactions” with the two students, calling them hundreds of times off-hours on her cellphone, according to schools investigator Richard Condon.

He called for Stringfellow to be disciplined, and urged termination of three co-workers – teachers Kendra Newkirk and Sharion Thomas and aide Tiffany Washington.

Instead of reporting swirling sex rumors to authorities, the three conducted their own probe, Condon said.

The DOE said it will put a letter of discipline in Stringfellow’s file and begin termination proceedings against Thomas and Washington, said spokesman Keith Kalb.

Newkirk was fired in July for unrelated reasons, Kalb said.

Stringfellow is no longer at Acorn, a city school with ties to the activist group. She is teaching Rikers Island inmates.

Thomas and Washington, who are still at Acorn, will be reassigned to off-campus jobs.

Condon said he believes there was no sex, but admitted that he couldn’t be 100 percent sure.

“Those things that we could verify, she [Stringfellow] was being truthful,” Condon said. “If this had been reported to us earlier, who knows, maybe we could have done some surveillance and found something else.”